Answer
There are 32 options for purchasing a house in Euclid Estates.
Work Step by Step
{pool, screened-in balcony, lake view, alarm system, upgraded landscaping}
As a person may purchase a house that contains any combination of the given options, including none or all the options, the number of options is going to be equal to the number of subsets.
A set of $n$ elements has $2^n$ subsets; therefore, our set has:
$2^5=32$ subsets.
There are 32 options for purchasing a house in Euclid Estates.
